Search NASA⌕ Search

SEARCH · Search NASA

Results for “RESEARCH TECHNIQUE, MATHEMATICS”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Bandwidth efficient coding: Theoretical limits and real achievements. Error control techniques for satellite and space communications

In his seminal 1948 paper 'The Mathematical Theory of Communication,' Claude E. Shannon derived the 'channel coding theorem' which has an explicit upper bound, called the channel capacity, on the rate at which 'information' could be transmitted reliably on a given communication channel. Shannon's result was an existence theorem and did not give specific codes to achieve the bound. Some skeptics have claimed that the dramatic performance improvements predicted by Shannon are not achievable in practice. The advances made in the area of coded modulation in the past decade have made communications engineers optimistic about the possibility of achieving or at least coming close to channel capacity. Here we consider the possibility in the light of current research results.

Costello, Daniel J., Jr.↗
NASA NTRS2004

Characterization and Uncertainty Analysis of a Reference Pressure Measurement System for Wind Tunnels

This paper presents the calibration results and uncertainty analysis of a high-precision reference pressure measurement system currently used in wind tunnels at the NASA Langley Research Center (LaRC). Sensors, calibration standards, and measurement instruments are subject to errors due to aging, drift with time, environment effects, transportation, the mathematical model, the calibration experimental design, and other factors. Errors occur at every link in the chain of measurements and data reduction from the sensor to the final computed results. At each link of the chain, bias and precision uncertainties must be separately estimated for facility use, and are combined to produce overall calibration and prediction confidence intervals for the instrument, typically at a 95% confidence level. The uncertainty analysis and calibration experimental designs used herein, based on techniques developed at LaRC, employ replicated experimental designs for efficiency, separate estimation of bias and precision uncertainties, and detection of significant parameter drift with time. Final results, including calibration confidence intervals and prediction intervals given as functions of the applied inputs, not as a fixed percentage of the full-scale value are presented. System uncertainties are propagated beginning with the initial reference pressure standard, to the calibrated instrument as a working standard in the facility. Among the several parameters that can affect the overall results are operating temperature, atmospheric pressure, humidity, and facility vibration. Effects of factors such as initial zeroing and temperature are investigated. The effects of the identified parameters on system performance and accuracy are discussed.

Amer, Tahani↗
NASA NTRS1989

A design philosophy for multi-layer neural networks with applications to robot control

A system is proposed which receives input information from many sensors that may have diverse scaling, dimension, and data representations. The proposed system tolerates sensory information with faults. The proposed self-adaptive processing technique has great promise in integrating the techniques of artificial intelligence and neural networks in an attempt to build a more intelligent computing environment. The proposed architecture can provide a detailed decision tree based on the input information, information stored in a long-term memory, and the adapted rule-based knowledge. A mathematical model for analysis will be obtained to validate the cited hypotheses. An extensive software program will be developed to simulate a typical example of pattern recognition problem. It is shown that the proposed model displays attention, expectation, spatio-temporal, and predictory behavior which are specific to the human brain. The anticipated results of this research project are: (1) creation of a new dynamic neural network structure, and (2) applications to and comparison with conventional multi-layer neural network structures. The anticipated benefits from this research are vast. The model can be used in a neuro-computer architecture as a building block which can perform complicated, nonlinear, time-varying mapping from a multitude of input excitory classes to an output or decision environment. It can be used for coordinating different sensory inputs and past experience of a dynamic system and actuating signals. The commercial applications of this project can be the creation of a special-purpose neuro-computer hardware which can be used in spatio-temporal pattern recognitions in such areas as air defense systems, e.g., target tracking, and recognition. Potential robotics-related applications are trajectory planning, inverse dynamics computations, hierarchical control, task-oriented control, and collision avoidance.

Vadiee, Nader↗
NASA NTRS1987

Status of the Mast experiment

Many sophisticated mathematical control techniques for flexible structures have been devised. The basic problem is that most of them require a relatively accurate mathematical model of the system under control including the dynamics of both the structure and the control system components. Obtaining such a model for either subsystem traditionally has required great effort including a significant validation step based on test data. Because of the quantum increase in complexity over proven methods, promising techniques for the control of flexible structures must be validated in actual hardware experiments before committing to their use in actual spacecraft missions. The Mast experiment system serves as a focus for such validation. It is the first in a series of experiments under the Control of Flexible Structures (COFS) Program at the NASA Langley Research Center. The Mast experiment is a combination of ground tests, orbital flight test, and analysis of a deployable beam under the COFS program. It provides a vehicle for research in structures, structural dynamics, and control issues.

Hanks, Brantley R.↗
NASA NTRS1992

Interferometric reconstruction of three-dimensional high-speed aerodynamic flows

Holographic interferometry can be a very useful diagnostic tool in high-speed aerodynamic testing. During this summer research period, various possible approaches for accurately reconstructing three-dimensional flows from limited data were examined. The approach based on the combination of the following three techniques appears to be promising: (1) Continuous Local Basis Function Method - this computational tomographic method has a power to accurately reconstruct continuous regions and is appropriate from well-conditioned to moderately limited data; (2) Variable Basis Method - this computational tomographic method provides accuracy near discontinuities, i.e., shock regions, and is appropriate from moderately-limited to severely-limited data; and (3) Complementary Field Method - this is a general iterative reconstructor that can be coupled with any computational tomographic techniques. Mathematically, it can be shown that this method can provide better accuracy than the direct reconstruction as in a conventional approach. Our numerical simulation of experiments demonstrated improved reconstruction results even when these techniques were individually tested.

Cha, Soyoung Stephen↗
NASA NTRS2016

Exploring the Use of Alfven Waves in Magnetometer Calibration at Geosynchronous Orbit

An Alfven wave is a type magnetohydrodynamicwave that travels through a conducting fluid under the influence of a magnetic field. Researchers have successfully calculated offset vectors of magnetometers in interplanetary space by optimizing the offset to maximize certain Alfvenic properties of observed waves (Leinweber, Belcher). If suitable Alfven waves can be found in the magnetosphere at geosynchronous altitude then these techniques could be used to augment the overall calibration plan for magnetometers in this region such as on the GOES spacecraft, possibly increasing the time between regular maneuvers. Calibration maneuvers may be undesirable because they disrupt the activities of other instruments. Various algorithms to calculate an offset using Alfven waves were considered. A new variation of the Davis-Smith method was derived because it can be mathematically shown that the Davis-Smith method tolerates filtered data, which expands potential applications. The variant developed was designed to find only the offset in the plane normal to the main field because the overall direction of Earth's magnetic field rarely changes, and theory suggests the Alfvenic disturbances occur transverse to the main field. Other variations of the Davis-Smith method encounter problems with data containing waves that propagate in mostly the same direction. A searching algorithm was then designed to look for periods of time with potential Alfven waves in GOES 15 data based on parameters requiring that disturbances be normal to the main field and not change field magnitude. Final waves for calculation were hand-selected. These waves produced credible two-dimensional offset vectors when input to the Davis-Smith method. Multiple two-dimensional solutions in different planes can be combined to get a measurement of the complete offset. The resulting three dimensional offset did not show sufficient precision over several years to be used as a primary calibration method, but reflected changes in the offset fairly well, suggesting that the method could be helpful in monitoring trends of the offset vector when maneuvers cannot be used.

calibration↗
NASA NTRS1986

A survey of functional programming language principles

Research in the area of functional programming languages has intensified in the 8 years since John Backus' Turing Award Lecture on the topic was published. The purpose of this paper is to present a survey of the ideas of functional programming languages. The paper assumes the reader is comfortable with mathematics and has knowledge of the basic principles of traditional programming languages, but does not assume any prior knowledge of the ideas of functional languages. A simple functional language is defined and used to illustrate the basic ideas. Topics discussed include the reasons for developing functional languages, methods of expressing concurrency, the algebra of functional programming languages, program transformation techniques, and implementations of functional languages. Existing functional languages are also mentioned. The paper concludes with the author's opinions as to the future of functional languages. An annotated bibliography on the subject is also included.

Holloway, C. M.↗
NASA NTRS1990

Noncontact measurement of high temperature using optical fiber sensors

The primary goal of this research program was the investigation and application of noncontact temperature measurement techniques using optical techniques and optical fiber methods. In particular, a pyrometer utilizing an infrared optical light pipe and a multiwavelength filtering approach was designed, revised, and tested. This work was motivated by the need to measure the temperatures of small metallic pellets (approximately 3 mm diameter) in free fall at the Microgravity Materials Processing Drop Tube at NASA Marshall Space Flight Center. In addition, research under this program investigated the adaptation of holography technology to optical fiber sensors, and also examined the use of rare-earth dopants in optical fibers for use in measuring temperature. The pyrometer development effort involved both theoretical analysis and experimental tests. For the analysis, a mathematical model based on radiative transfer principles was derived. Key parameter values representative of the drop tube system, such as particle size, tube diameter and length, and particle temperature, were used to determine an estimate of the radiant flux that will be incident on the face of an optical fiber or light pipe used to collect radiation from the incandescent falling particle. An extension of this work examined the advantage of inclining or tilting the collecting fiber to increase the time that the falling particle remains in the fiber field-of-view. Those results indicate that increases in total power collected of about 15 percent may be realized by tilting the fiber. In order to determine the suitability of alternative light pipes and optical fibers, and experimental set-up for measuring the transmittance and insertion loss of infrared fibers considered for use in the pyrometer was assembled. A zirconium fluoride optical fiber and several bundles of hollow core fiber of varying diameters were tested. A prototype two-color pyrometer was assembled and tested at Virginia Tech, and then tested on the Drop Tube at Marshall Space Flight Center. Radiation from 5 mm diameter niobium drops falling in the Drop Tube was successfully detected, and recorded for later analysis. Subsequent analysis indicated that the imaging of light output from the light pipe onto the detector active areas was not identical for both detectors.

Claus, R. O.↗
NASA NTRS1985

Mathematical analysis study for radar data processing and enhancement. Part 1: Radar data analysis

A study is performed under NASA contract to evaluate data from an AN/FPS-16 radar installed for support of flight programs at Dryden Flight Research Facility of NASA Ames Research Center. The purpose of this study is to provide information necessary for improving post-flight data reduction and knowledge of accuracy of derived radar quantities. Tracking data from six flights are analyzed. Noise and bias errors in raw tracking data are determined for each of the flights. A discussion of an altiude bias error during all of the tracking missions is included. This bias error is defined by utilizing pressure altitude measurements made during survey flights. Four separate filtering methods, representative of the most widely used optimal estimation techniques for enhancement of radar tracking data, are analyzed for suitability in processing both real-time and post-mission data. Additional information regarding the radar and its measurements, including typical noise and bias errors in the range and angle measurements, is also presented. This is in two parts. This is part 1, an analysis of radar data.

James, R.↗
NASA NTRS1992

Linear Spectral Analysis of Plume Emissions Using an Optical Matrix Processor

Plume spectrometry provides a means to monitor the health of a burning rocket engine, and optical matrix processors provide a means to analyze the plume spectra in real time. By observing the spectrum of the exhaust plume of a rocket engine, researchers have detected anomalous behavior of the engine and have even determined the failure of some equipment before it would normally have been noticed. The spectrum of the plume is analyzed by isolating information in the spectrum about the various materials present to estimate what materials are being burned in the engine. Scientists at the Marshall Space Flight Center (MSFC) have implemented a high resolution spectrometer to discriminate the spectral peaks of the many species present in the plume. Researchers at the Stennis Space Center Demonstration Testbed Facility (DTF) have implemented a high resolution spectrometer observing a 1200-lb. thrust engine. At this facility, known concentrations of contaminants can be introduced into the burn, allowing for the confirmation of diagnostic algorithms. While the high resolution of the measured spectra has allowed greatly increased insight into the functioning of the engine, the large data flows generated limit the ability to perform real-time processing. The use of an optical matrix processor and the linear analysis technique described below may allow for the detailed real-time analysis of the engine's health. A small optical matrix processor can perform the required mathematical analysis both quicker and with less energy than a large electronic computer dedicated to the same spectral analysis routine.

Gary, C. K.↗
NASA NTRS1985

Mathematical analysis study for radar data processing and enchancement. Part 2: Modeling of propagation path errors

A study is performed under NASA contract to evaluate data from an AN/FPS-16 radar installed for support of flight programs at Dryden Flight Research Facility of NASA Ames Research Center. The purpose of this study is to provide information necessary for improving post-flight data reduction and knowledge of accuracy of derived radar quantities. Tracking data from six flights are analyzed. Noise and bias errors in raw tracking data are determined for each of the flights. A discussion of an altitude bias error during all of the tracking missions is included. This bias error is defined by utilizing pressure altitude measurements made during survey flights. Four separate filtering methods, representative of the most widely used optimal estimation techniques for enhancement of radar tracking data, are analyzed for suitability in processing both real-time and post-mission data. Additional information regarding the radar and its measurements, including typical noise and bias errors in the range and angle measurements, is also presented. This report is in two parts. This is part 2, a discussion of the modeling of propagation path errors.

James, R.↗
NASA NTRS1981

Remote sensing of temperature profiles in vegetation canopies using multiple view angles and inversion techniques

A mathematical method is presented which allows the determination of vertical temperature profiles of vegetation canopies from multiple sensor view angles and some knowledge of the vegetation geometric structure. The technique was evaluated with data from several wheat canopies at different stages of development, and shown to be most useful in the separation of vegetation and substrate temperatures with greater accuracy in the case of intermediate and dense vegetation canopies than in sparse ones. The converse is true for substrate temperatures. Root-mean-square prediction accuracies of temperatures for intermediate-density wheat canopies were 1.8 C and 1.4 C for an exact and an overdeterminate system, respectively. The findings have implication for remote sensing research in agriculture, geology or other earth resources disciplines.

Kimes, D. S.↗
NASA NTRS1993

A robust rotorcraft flight control system design methodology utilizing quantitative feedback theory

Rotorcraft flight control systems present design challenges which often exceed those associated with fixed-wing aircraft. First, large variations in the response characteristics of the rotorcraft result from the wide range of airspeeds of typical operation (hover to over 100 kts). Second, the assumption of vehicle rigidity often employed in the design of fixed-wing flight control systems is rarely justified in rotorcraft where rotor degrees of freedom can have a significant impact on the system performance and stability. This research was intended to develop a methodology for the design of robust rotorcraft flight control systems. Quantitative Feedback Theory (QFT) was chosen as the basis for the investigation. Quantitative Feedback Theory is a technique which accounts for variability in the dynamic response of the controlled element in the design robust control systems. It was developed to address a Multiple-Input Single-Output (MISO) design problem, and utilizes two degrees of freedom to satisfy the design criteria. Two techniques were examined for extending the QFT MISO technique to the design of a Multiple-Input-Multiple-Output (MIMO) flight control system (FCS) for a UH-60 Black Hawk Helicopter. In the first, a set of MISO systems, mathematically equivalent to the MIMO system, was determined. QFT was applied to each member of the set simultaneously. In the second, the same set of equivalent MISO systems were analyzed sequentially, with closed loop response information from each loop utilized in subsequent MISO designs. The results of each technique were compared, and the advantages of the second, termed Sequential Loop Closure, were clearly evident.

Gorder, Peter James↗
NASA NTRSDate not supplied

Comparison and Application of Battery Modeling Methods for Conceptual Electric Aircraft

Growing interest in design and optimization of electrified aircraft propulsion concepts prompts the need for accurate, flexible, and efficient methods to model battery systems. Presented in this paper are three battery modeling methods that have been used at NASA’s Glenn Research Center, each representing different mathematical or electrical approaches. Thévenin equivalent circuit, normalization, and curve-fitting methods are compared against battery cell test data for the X-57 Maxwell electric aircraft technology demonstrator. The methods are then applied in a simple multidisciplinary optimization context using NASA’s Six-Passenger Electric Quadrotor concept to determine their applicability and performance. The normalization method achieves the highest accuracy for steady and unsteady discharge rates with a voltage mean error percentage of 0.423% and 1.186%, respectively. Optimal quadrotor mission range between the models varies up to 0.5 nmi, identifying current battery modeling methods as a potentially significant contributor to mission analysis error. A set of relevant tools and techniques for conceptual battery modeling are identified in this paper, with conclusions made on the utility of each modeling approach for various design challenges.

power↗
NASA NTRS1997

A Model for Space Shuttle Orbiter Tire Side Forces Based on NASA Landing Systems Research Aircraft Test Results

Forces generated by the Space Shuttle orbiter tire under varying vertical load, slip angle, speed, and surface conditions were measured using the Landing System Research Aircraft (LSRA). Resulting data were used to calculate a mathematical model for predicting tire forces in orbiter simulations. Tire side and drag forces experienced by an orbiter tire are cataloged as a function of vertical load and slip angle. The mathematical model is compared to existing tire force models for the Space Shuttle orbiter. This report describes the LSRA and a typical test sequence. Testing methods, data reduction, and error analysis are presented. The LSRA testing was conducted on concrete and lakebed runways at the Edwards Air Force Flight Test Center and on concrete runways at the Kennedy Space Center (KSC). Wet runway tire force tests were performed on test strips made at the KSC using different surfacing techniques. Data were corrected for ply steer forces and conicity.

Carter, John F.↗
NASA NTRS1999

High Order Approximations for Compressible Fluid Dynamics on Unstructured and Cartesian Meshes

The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining challenges facing the field of computational fluid dynamics. In structural mechanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the computation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order accuracy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence suggests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Center. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18, 1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25, 1998 at the NASA Ames Research Center in the United States. During this special course, lecturers from Europe and the United States gave a series of comprehensive lectures on advanced topics related to the high-order numerical discretization of partial differential equations with primary emphasis given to computational fluid dynamics (CFD). Additional consideration was given to topics in computational physics such as the high-order discretization of the Hamilton-Jacobi, Helmholtz, and elasticity equations. This volume consists of five articles prepared by the special course lecturers. These articles should be of particular relevance to those readers with an interest in numerical discretization techniques which generalize to very high-order accuracy. The articles of Professors Abgrall and Shu consider the mathematical formulation of high-order accurate finite volume schemes utilizing essentially non-oscillatory (ENO) and weighted essentially non-oscillatory (WENO) reconstruction together with upwind flux evaluation. These formulations are particularly effective in computing numerical solutions of conservation laws containing solution discontinuities. Careful attention is given by the authors to implementational issues and techniques for improving the overall efficiency of these methods. The article of Professor Cockburn discusses the discontinuous Galerkin finite element method. This method naturally extends to high-order accuracy and has an interpretation as a finite volume method. Cockburn addresses two important issues associated with the discontinuous Galerkin method: controlling spurious extrema near solution discontinuities via "limiting" and the extension to second order advective-diffusive equations (joint work with Shu). The articles of Dr. Henderson and Professor Schwab consider the mathematical formulation and implementation of the h-p finite element methods using hierarchical basis functions and adaptive mesh refinement. These methods are particularly useful in computing high-order accurate solutions containing perturbative layers and corner singularities. Additional flexibility is obtained using a mortar FEM technique whereby nonconforming elements are interfaced together. Numerous examples are given by Henderson applying the h-p FEM method to the simulation of turbulence and turbulence transition.

Barth, Timothy↗
NASA NTRS2026

Development of a One-Domain Volume-Averaged Navier–Stokes Solver

The interaction between a high-enthalpy flow and a thermal protection material is inherently multiscale and multiphysics. In conventional aerothermal analyses, the external flow and material response are generally modeled using separate computational domains coupled through boundary conditions at the material surface. Although this approach has supported many practical applications, it requires assumptions about the location and behavior of the interface and may become difficult to apply when material decomposition, internal reactions, and surface recession substantially alter the porous structure. This report presents the development of a one-domain formulation in which the free-fluid and porous-material regions are represented within a single computational domain. The formulation is based on the volume-averaged Navier–Stokes (VANS) equations, derived from the governing equations for reacting, compressible flow and condensed material. Volume averaging transfers the influence of the unresolved material microstructure to the macroscale equations through effective transport properties, interfacial source terms, and dispersion fluxes. Particular attention is given to regions in which porosity and permeability vary rapidly, including the diffuse transition between a porous material and the surrounding fluid. The resulting equations are implemented in the Porous-material Analysis Toolbox based on OpenFOAM (PATO). The report describes the pressure–velocity coupling strategy used by the solver, examines spatial filtering techniques for deriving effective properties, and evaluates the influence of a smoothly varying interface permeability. Numerical demonstrations include canonical porous-flow configurations, a flow-tube configuration representative of FiberForm® permeability experiments, and the oxidation of a porous carbon material. The purpose of this work is to establish a mathematical and computational foundation for a unified treatment of flow and thermal protection material response. The present formulation is intended to support the progressive inclusion of additional physical processes, including multicomponent transport, finite-rate gas–surface chemistry, pyrolysis, internal oxidation, and material recession. It also provides a framework for connecting pore-scale simulations and microstructural characterization with macroscale aerothermal-response calculations. This report is intended for researchers and engineers working in computational fluid dynamics, porous-media transport, material response, and thermal protection system modeling. It documents both the theoretical development and the initial numerical assessment of the one-domain approach, while identifying the closure of effective and dispersion terms as an important subject for continued investigation.

Ablation↗
NASA NTRS1981

Self-induced wing rock of slender delta wings

As part of a research program aimed at exploring basic mechanisms that cause wing rock in combat aircraft, an investigation was conducted to study the aerodynamic factors which cause the low-speed wing rock exhibited by slender delta wings. A flat-plate delta wing with 80 deg leading-edge sweep was subjected to conventional static-force tests and dynamic wind-tunnel experiments which included forced-oscillation, rotary, and free-to-roll tests. In addition, visualization of the flow phenomena involved was obtained by observing tuft patterns and using a helium-bubble technique. This paper summarizes the results of this study. Fundamental information is presented on the aerodynamic mechanisms that cause the wing rock and the problem of mathematically modeling the aerodynamics and motions is discussed.

Nguyen, L. T.↗